The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Nov 05 2025 15:22:30
%S 1,1,1,1,2,4,4,7,9,11,16,23,31,40,53,71,91,121,161,206,264,343,441,
%T 563,725,922,1166,1476,1869,2357,2967,3725,4659,5816,7263,9050,11241,
%U 13947,17269,21333,26342,32479,39957,49094,60231,73775,90273,110333,134643
%N Expansion of Product_{k>=1} ((1+x^(3*k-1))*(1+x^(3*k-2)))^k.
%C Convolution of A262878 and A262879.
%H Vaclav Kotesovec, <a href="/A262884/b262884.txt">Table of n, a(n) for n = 0..2000</a>
%H Vaclav Kotesovec, <a href="https://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015
%F a(n) ~ exp(-Pi^4/(2592*Zeta(3)) + Pi^2 * n^(1/3) / (12*3^(2/3)*Zeta(3)^(1/3)) + 3^(2/3) * Zeta(3)^(1/3) * n^(2/3)/2) * Zeta(3)^(1/6) / (2^(7/18) * 3^(2/3) * sqrt(Pi) * n^(2/3)).
%t nmax = 50; CoefficientList[Series[Product[((1+x^(3*k-1))*(1+x^(3*k-2)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A262878, A262879, A262883, A262924.
%K nonn
%O 0,5
%A _Vaclav Kotesovec_, Oct 04 2015